Ionic polymer transducers (IPTs) are fabricated from ionomers sandwiched between conductive electrodes. IPTs act as actuators by deforming in response to an input voltage. They also exhibit sensing behavior yielding a current when exposed to various forms of deformation. IPT performance depends on many variables including the stiffness of the polymer which evolves with the level of semicrystallinity within the polymer. The purpose of this study is to investigate the strength of the streaming potential model for IPTs created with polymers having various semicrystallinity percentages. Specifically in this case, annealing effects, which influence the semicrystallinity and stiffness of the polymer, on IPT sensing were explored in bending. The implications of streaming potential theory on current generation presented here will be evaluated via experiments that will be discussed in a later publication. The model proposed here is different than previous reports on the streaming potential theory because incorporation of two very important variables has not been considered before: semicrystallinity and time. It is shown that the semicrystallinity especially is a key factor.

Ionic Polymer Transducers (IPTs) have both actuation and sensing capabilities. However, the electromechanical
response of an IPT as a sensor is quite different from the response as an actuator. IPT sensors are not limited to
bending, i.e., they also produce current for compressive, extensional, and shear deformations. A robust physical
model must be able to predict the existence of a sensing signal in all modes of deformation. Such a model could
subsequently be adapted to form a roadmap toward enhancing sensitivity. In this study, the objective is to
experimentally define IPT sensing characteristics in shear deformation (non-bending) and compare the empirical
results with predictions derived from a model based on the streaming potential hypothesis. An in-house
displacement control rig is employed to establish empirical results in shear sensing. A finite element approach is
employed in the companion model development. The IPTs considered employ Nafion as the ionic polymer layer,
while the electrode includes high surface area ruthenium oxide, RuO2, metallic powder and deposited per the Direct
Assembly Process.

An ionic polymer transducer (IPT) may be employed as either an actuator or sensor, where the bending mode of transduction has frequently been studied. However, the electromechanical response is not symmetric; the voltage signal required to induce a given tip displacement in actuation is higher than that generated for the same deformation in sensing by an order of magnitude or more. Thus the physical mechanisms responsible for actuation and sensing are necessarily different. Because IPTs display sensing response for any mode of deformation (bending, tension, compression, shear), it is postulated that the mechanism of streaming potential dominates sensing response. The source of the streaming potential is the flow of entrained fluid and cations (electrolyte) with respect to the electrodes expected for any mode of deformation. In this study flow is assumed to be linear and Newtonian. Trends in the flow due to imposed shear are investigated. Implications of these trends in relation to physical regions of the polymer nanochannels will be explored

Stiffness variation versus stimulation for a light activated shape memory polymer (LASMP) is predicted with a
multiscale modeling approach. The multiscale model utilizes rotational isomeric state theory to build a polymer chain
conformation, Johnson distributions to model the distances between crosslinks, junction constraints to model
neighboring chain interactions, and Boltzmann statistical mechanics to relate the entropy of the chain to the macroscopic
response. It is shown that a novel choice for the equation describing stress dependence on strain, capturing the
polymer's departure from affine deformation, results in a stress strain curve with an expected shape. The fitting
parameters characterizing the interaction with neighboring chains can also be phenomenologically fit to experimental
data, yielding accurate modulus predictions. The result is a bottom up model accurately predicting the material response
of the polymer with parameters that can be derived almost entirely from the molecular formula of the polymer, allowing
sufficiently similar polymers to be modeled accurately, reducing the time, effort, and resources required in the
development of new polymer systems.

A streaming potential method for modeling the electromechanical responses due to imposed deformation of ionic
polymer transducers (IPTs) is presented. It has been argued that imperfect ion pairing results in the availability of free
counterions within the hydrophilic regions, thereby resulting in the presence of an electrolyte within these regions in the
hydrophobic polymer matrix. When there is a net relative motion of this electrolyte with respect to the electrode, a
streaming potential should result. It is hypothesized that a streaming potential mechanism within the electrode regions
should be able to predict sensing responses for all modes of deformation. Based on a recently introduced parallel waterchannel
morphology in Nafion® membrane, this model successfully addresses the physics of sensing in IPT bending. A
linear relationship between the tip deflection of an IPT cantilever beam and the current generated in the IPT is achieved.
The result trends show a good agreement with the experimental measurements. While this work studies the bending
mode, it is able to be adapted for the other three sensing modes.

While the acidic polymer electrolyte membrane (PEM) Nafion has garnered considerable attention, the active response
of basic PEMs offers another realm of potential applications. For instance, the basic PEM Selemion is currently being
considered in the development of a CO<sub>2</sub> separation prototype device to be employed in coal power plant flue gas. The
mechanical integrity of this material and subsequent effects in active response in this harsh environment will become
important in prototype development. A multiscale modeling approach based on rotational isomeric state theory in
combination with a Monte Carlo methodology may be employed to study mechanical integrity. The approach has the
potential to be adapted to address property change of any PEM in the presence of foreign species (reinforcing or
poisoning), as well as temperature and hydration variations. The conformational characteristics of the Selemion
polymer chain and the cluster morphology in the polymer matrix are considered in the prediction of the stiffness of
Selemion in specific states.

Rotational isomeric state (RIS) theory has long been used to predict mechanical response trends in polymeric materials
based on the polymer chain conformation it addresses. Successful adaptation of this methodology to the prediction of
elastic moduli would provide a powerful tool for guiding ionomer fabrication. Recently, a multiscale modeling approach
to the material stiffness prediction of ionic polymer has been developed. It applies traditional RIS theory in combination
with a Monte Carlo methodology to develop a simulation model for polymer chain conformation on a nanoscopic level.
A large number of end-to-end chain lengths are generated from this model and are then used to estimate the probability
density function which is used as an input parameter to enhance existing energetics-based macroscale models of ionic
polymer for material stiffness prediction. This work improves this Mark-Curro Monte Carlo methodology by adapting
the RIS theory in a way to overcome early terminations of polymer chain while simulating the conformation of polymer
chains and thus obtains more realistic values of chain length. One solvated Nafion<sup>®</sup> case is considered. The probability
density function for chain length is estimated with the most appropriate Johnson family method applied. The stiffness
prediction is considered as a function of total molecular weight.

In order to provide structures with new and better characteristics, researchers often look to biological systems for
inspiration. One trait that many biological system have that conventional structures do not is a circulatory system, which
can be used for many purposes, one of which is the transport of structural material. This paper explores the benefits of
transporting structural material for the purpose of changing the structure's static and dynamic characteristics. Several
scenarios are explored, including the transport of non-load-bearing mass (mass transport) to load-bearing mass (termed
stiffness transport). It is argued that stiffness transport, while more complex than simply moving mass within a
structure, affords the same features as mass transport, along with several unconventional and particularly useful abilities.

Nastic materials are high energy density active materials that mimic processes used in the plant kingdom to produce large deformations through the conversion of chemical energy. These materials utilize the controlled transport of charge and fluid across a selectively-permeable membrane to achieve bulk deformation in a process referred to in the plant kingdom as <i>nastic movements</i>. The nastic material being developed consists of synthetic membranes containing biological ion pumps, ion channels, and ion exchangers surrounding fluid-filled cavities embedded within a polymer matrix. In this paper the formulation of a biological transport model and its coupling with a hyperelastic finite element model of the polymer matrix is discussed. The transport model includes contributions from ion pumps, ion exchangers, and solvent flux. This work will form the basis for a feedback loop in material synthesis efforts. The goal of these studies is to determine the relative importance of the various parameters associated with both the polymer matrix and the biological transport components.

Application of Rotational Isomeric State (RIS) theory to the
prediction of Young's modulus of a solvated ionomer is considered.
RIS theory directly addresses polymer chain conformation as it
relates to mechanical response trends. Successful adaptation of
this methodology to the prediction of elastic moduli would thus
provide a powerful tool for guiding ionomer fabrication. The
Mark-Curro Monte Carlo methodology is applied to generate a
statistically valid number of end-to-end chain lengths via RIS
theory for a solvated Nafion case. The distribution of chain
lengths is then fitted to a Probability Density Function by the
Johnson Bounded distribution method. The fitting parameters, as
they relate to the model predictions and physical structure of the
polymer, are studied so that a means to extend RIS theory to the
reliable prediction of ionomer stiffness may be identified.

A computational micromechanics model applying Monte Carlo methodology has been developed to predict the equilibrium state of a single cluster of an ionomeric polymer with cluster morphology. No assumptions are made regarding the distribution of charge or the shape of the cluster. Assuming a constant solvated state, the model tracks the position of individual ions within a given cluster in response to ion-ion interaction, mechanical stiffness of the pendant chain, cluster surface energy, and external electric field loading. Expressions are developed to directly account for forces imposed on ions due to ion-cluster surface interaction. The model is applied to study the impact of counterion size. Predictions suggest that smaller counterions lead to a system which better facilitates ion transport than larger counterions. Results further suggest that, regardless of ion size, ion pairing is rarely complete; this in turn suggests that the classic assumptions will tend to under-predict electromechanical actuation response in general.

It has recently been theorized that the initial fast electro-mechanical response of ionic-polymer-metal composites (IPMCs) may be due to a polarization mechanism, while transport dominates the relaxation response. In order to investigate this hypothesis, a computational micromechanics model has been developed to model polarization response in these ionomeric transducers. Assuming a constant solvated state, the model tracks the rotation of individual dipoles within a given cluster in response to dipole-dipole interaction, mechanical stiffness of the pendant chain, and external electrical field loading. Once the system of dipoles reaches equilibrium in response to loading, net polarization/distortion response is recorded. Actuation predictions using the polarization model are consistent with the experimentally observed fast response of these materials.

A micro-electro-mechanical model of the behavior of piezoelectric ceramics including thermal, and rate effects is presented and compared to experimental data. Results include analytical and numerical investigations of the behavior of piezoelectric ceramics. The model is based on physical mechanisms and includes elastic, dielectric, and piezoelectric anisotropy. Moreover, the model is based on an internal energy approach so that work-energy relations may be directly applied. Results from the model give insight into material behavior.

A system dynamic model has been developed for assessing the performance of a piezoelectric hydraulic pump. The pump system comprises a stack actuator driven pump, four-way valve, hydraulic accumulator, and hydraulic actuator. A system of differential equations was developed that governs the electrical / mechanical / fluid coupled behavior. The system of equations was simultaneously solved using MATLAB. The results were compared to pump data for a stack actuator input of 2 MV/m at operating frequencies between 2.5 Hz and 100 Hz. Previous work comparing the model to experimental results was recently accepted for publication in a future article . The work presented below presents a review of the model and discusses additional experimental results of the pump's flow rate response under hydraulic actuator loads. The model achieved reasonable agreement with flow rate measurements when the hydraulic actuator was loaded with 62 N and 142 N of constant force. Rate effects were observed to limit the high frequency performance. These effects were attributed to fluid compressibility, check valve resistance, and self heating of the stack actuator. The model provides a design tool for evaluating bandwidth limitations and increasing pressure and flow rate.

A piezohydraulic pump making use of the step and repeat capability of piezoelectric actuators has been developed for actuation of aircraft control surfaces. The piezohydraulic pump utilizes a piezoelectric stack actuator to drive a piston in a cylinder. The cylinder is fitted with two check valves. On the compression stroke, oil is forced out of the cylinder. On the intake stroke, oil is drawn into the cylinder. The oil is used to drive a linear actuator. The actuator was driven at 7cm/sec with a 271N (61lb) blocking force. To achieve this, the piezoelectric stack actuator was driven at 60Hz with a switching power supply. The system utilizes an accumulator to eliminate cavitation. This work discusses piezohydraulic pumping theory, pump design, and pump performance. Consideration of pump performance includes the effects of varying accumulator pressure, hydraulic oil viscosity, and load imposed on the linear actuator.

Recent research in smart wing technology has led to the identification of a need for large displacement (0.1 to 10 mm), high force (10 to 2000 N) actuators that function over low to intermediate frequency bands (0.1 to 200 Hz). A hybrid piezohydraulic pump is under development for this smart structures application. Piezoelectric stack actuators are capable of producing large forces at higher bandwidth, but the stroke is too small. Shape memory alloys are capable of producing a larger stroke, but the bandwidth is too low. Step and repeat piezoelectric devices, such as inchworm motors, increase the power output of the actuators and have the potential to produce large forces and large displacements simultaneously. The piezohydraulic pump makes use of the step and repeat capability. A preliminary piezoelectric stack actuator driven hydraulic pumps system was constructed. The pump was connected to a hydraulic actuator and the actuator driven at 1 cm/sec with a 490 N (110 lb) blocking force. To achieve this, the stack actuator was driven at 10 Hz. Two subsequent generations of the piezohydraulic pump achieved intermittent actuation rates of 10 cm/sec. This work presents efficiency considerations and design modifications utilized in the subsequent generations of the piezohydraulic pump. The relationship between the diameter of the hydraulic actuator, actuation rate, and blocking force are discussed. Effective use of accumulators to increase actuation rate and control bias pressure is also discussed.

A hybrid piezohydraulic pump is under development for smart structures applications. Structural control applications often require large force be delivered over a large displacement. Piezoelectric actuators produce a large force over a small displacement. This can be repeated many times per second. Step and repeat piezoelectric devices, such as inchworm motors, increase the power output of the actuators and have the potential to produce large forces and large displacements simultaneously. The piezohydraulic pump makes use of the step and repeat capability. The pump utilizes a piezoelectric stack actuator to drive a piston in a cylinder. The forward stroke pressurizes the hydraulic fluid in the cylinder and forces it out through a check valve. The reverse stroke draws fluid into the cylinder through a second check valve. The prototype pump has produced a working pressure of 6.9 MPa (1000 psi) and a flow rate of 45 ccm.

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